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Statistical Significance of Clustering using Soft Thresholding
Covariance Estimation High Dimension Invariance Principles Unsupervised Learning
2013/6/14
Clustering methods have led to a number of important discoveries in bioinformatics and beyond. A major challenge in their use is determining which clusters represent important underlying structure, as...
We consider the problem of clustering noisy high-dimensional data points into a union of low-dimensional subspaces and a set of outliers. The number of subspaces, their dimensions, and their orientati...
A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems
A General Iterative Shrinkage Thresholding Algorithm Non-convex Regularized Optimization Problems
2013/5/2
Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterp...
Subspace Clustering via Thresholding and Spectral Clustering
Subspace Clustering Thresholding Spectral Clustering
2013/5/2
We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown...
Block Thresholding on the Sphere
Block Thresholding Needlets Spherical Data Nonpara-metric Regression
2013/4/27
Th aim of this paper is to study the nonparametric regression estimators on the sphere built by the needlet block thresholding. The block thresholding procedure proposed here follows the method introd...
Grouping Strategies and Thresholding for High Dimensional Linear Models
Structured sparsity Grouping, Learning Theory Non Linear Methods Block-thresholding coherence Wavelets
2012/9/19
The estimation problem in a high regression model with structured sparsity is investigated.An algorithm using a two steps block thresholding procedure called GR-LOL is provided.Convergence rates are p...
On false discovery rate thresholding for classification under sparsity
false discovery rate thresholding classification under sparsity
2011/7/6
We study the properties of false discovery rate (FDR) thresholding, viewed as a classification procedure. The "0"-class (null) is assumed to have a known, symmetric log-concave density while the "1"-c...
Distributional Results for Thresholding Estimators in High-Dimensional Gaussian Regression Models
Markov chain Monte Carlo Hamiltonian dynamics Bayesian analysis
2011/7/6
We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with ...
Adaptive estimation in the nonparametric random coefficients binary choice model by needlet thresholding
Discrete choice models random coefficients inverse problems
2011/7/6
In this article we consider the estimation of the joint distribution of the random coefficients and error term in the nonparametric random coefficients binary choice model. In this model from economic...
Sparse linear discriminant analysis by thresholding for high dimensional data
Classification high dimensionality misclassification rate nor-mality optimal classification rule sparse estimates
2011/6/20
In many social, economical, biological and medical studies, one
objective is to classify a subject into one of several classes based on
a set of variables observed from the subject. Because the prob...
Adaptive Thresholding for Sparse Covariance Matrix Estimation
constrained ℓ 1 minimization covariance matrix Frobenius norm Gaus-sian graphical model rate of convergence precision matrix spectral norm
2011/3/21
In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven...
Perfect simulation using dominated coupling from the past with application to area-interaction point processes and wavelet thresholding
coupling from the past (CFTP) dominated CFTP exact simulation local stability Markov chain Monte Carlo perfect simulation
2010/3/11
We consider perfect simulation algorithms for locally stable point processes
based on dominated coupling from the past, and apply these methods
in two different contexts. A new version of the algori...
Wavelet block thresholding for samples with random design: A minimax approach under the Lp risk
Regression with random design wavelets block thresholding
2009/9/18
We consider the regression model with (known) random design. We investigate the minimax performances of an adaptive wavelet block thresholding estimator under the Lp risk with p >2 over Besov balls. W...
On the performances of a new thresholding procedure using tree structure
Besov spaces estimation maxiset minimax risk rate of convergence thresholding methods tree structure
2009/9/16
This paper deals with the problem of function estimation. Using the white noise model setting, we provide a method to construct a new wavelet procedure based on thresholding rules which takes advantag...
Thresholding-based iterative selection procedures for model selection and shrinkage
Sparsity nonconvex penalties thresholding model selection & shrinkage lasso ridge SCAD
2009/9/16
This paper discusses a class of thresholding-based iterative selection procedures (TISP) for model selection and shrinkage. People have long before noticed the weakness of the convex $l_1$-constraint ...